The Horizon programme, “Who’s Afraid of a Big Black Hole?” was broadcast on 3rd November 2009. In a very clear and lucid account, the programme brings us up-to-date, on the state of science regarding the densest concentrations of mass in our Universe. After explaining the major advances, the programme focuses on difficulties in the theory relating to the singularity: that point at the centre of a black hole into which matter relentlessly cascades. Because it is an infinitesimal point, gravitation converges to infinity there; and as it stands, physical theory breaks down.
The converging gravitational field and the singularity was predicted by Einstein’s General Theory of Relativity, but because the singularity is a microscopic object, in its vicinity, Quantum Mechanics must also be satisfied. Nevertheless, for some decades, theorists have struggled without success to unify these two theories, and the programme concludes with those eminent scientists contributing to the programme, expressing their bemused but determined puzzlement as to where they should turn for inspiration on how to form one theory from the two.
While watching the programme, I knew I must make cosmologists aware of the idea that motivated my own studies, an idea of some merit and substance, because that idea has resulted in a thesis that derives the logic of Quantum Mechanics. It was this: questions along the lines: “What Physical Laws brought about The Beginning?” are misplaced on grounds of logic. No true beginning can have laws that precede it. Otherwise, what rules generated those laws… and so on, ad infinitum.
It was this thought, in 1997, that led me to consider the possibility of self-reference in physics. A friend then pointed me in the direction of Kurt Gödel’s theorems and they naturally led to a search for mathematical undecidability in Quantum Mechanics.
In the Horizon programme, parallels are drawn between the singularities of black holes and another singularity with similar conditions: the one from which the Big Bang exploded. Now of course, the singularity of the Big Bang may not have been The Beginning; but if it was we should not expect to find Physical Laws to have brought it about.
A logical alternative to this is that the Matter, the Spacetime and the Physical Laws all came into existence together in a self referent loop where each initiates the other: a loop that would otherwise have been hovering in some undecidable state.
Since 2006 I have had extremely good success in finding mathematical undecidability at the core of quantum mathematics. This has a logical form where products of orthogonal vectors are not axiomatic; yet the Field Axioms, the rules of addition and multiplication for scalar components of all mathematical objects, neither forbid nor accommodate these products.
Quantum Mechanics then develops into a theory that tells us where indeterminacy comes from, what happens to it at measurement, why the world we witness is real, the reason for particles, and why probability is not indeterminate. There are also signs that the indeterminacy of chaos follows from a related but quite separate undecidability. Most remarkably, once seen in terms of its logical form, Quantum Mechanics becomes an elegantly intuitive theory.
Mathematical undecidability lies within systems whose operation has no option but to follow a deficient set of rules. My suggestion is that at the singularity there is such deficiency and that this is a good candidate worthy of investigation.